This study investigates evidence of non-compensatory preferences by incorporating attribute cutoffs into the modeling of consumer choices in the context of food with health-related attributes (omega-3 content) that may be associated with fortification or may result from genetic modification (GM). Data for this study were collected through a nation-wide internet-based survey drawn from a representative panel of Canadian households maintained by a major North American marketing firm. In addition to querying respondents on their perceptions and attitudes regarding food and health, choices of canola oils are elicited using a stated choice experiment in which product alternatives are identified based on attributes of price, country of origin, omega-3 content and GM/non-GM derivation. Consumers’ choices for functional canola oil products are examined in three steps. Initially, a conditional logit (CL) model is estimated assuming that no cutoffs apply in decisions on canola oil choices. Respondent’s self-reported cutoffs are then incorporated into the CL model and a random parameters logit (RPL) model, applying a utility model which penalizes rather than eliminates a desired alternative when a cutoff violation occurs. In the third step, the problem of endogeneity associated with attribute cutoffs is examined by linking respondents’ self-reported cutoffs to their demographic characteristics. Results from estimations of models with/without cutoffs show that consumers value omega-3 content in canola oils but dislike GM-derived ingredients in canola oil products. These Canadian respondents prefer canola oils produced in Canada to those produced in the United States. Regarding attribute cutoffs, it is found that consumers suffer a utility loss when violating their self-reported attribute cutoffs. Comparisons between models with/without attribute cutoffs suggest that incorporating cutoffs into the compensatory utility model significantly improves the model fit. Cutoff endogeneity is examined by predicting cutoffs based on respondents’ demographic characteristics. Using predicted cutoffs as instruments for self-reported cutoffs, this study provides some evidence that self-reported cutoffs may be endogenous and that researchers should consider using approaches that account for the potential endogeneity.